TY - JOUR
AU - V. D. Zalizko
PY - 2007/01/25
Y2 - 2024/06/14
TI - Coconvex approximation of periodic functions
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 59
IS - 1
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3290
AB - The Jackson inequality E n (f ) ≤ c ω 3 (f , π / n )connects the value of the best uniform approximation E n (f ) of a 2π-periodic function f : R → R by trigonometric polynomials of order ≤ n — 1 with its third modulus of continuity ω 3 (f, t ). In the present paper, we show that this inequality is true if continuous 2π-periodic functions that change their convexity on [—π, π) only at every point of a fixed finite set consisting of the even number of points are approximated by polynomials coconvex to them.
ER -